What are the components of the vector between the origin and the polar coordinate $(2, (-11pi)/6)$ ?

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Answer 1 · 2016-09-26T04:46:44

$(sqrt 3, 1)$

The components of the position vector to $r, theta) are (r cos theta, r sin theta)$

Here, they are

$(2 cos(-11/6pi), 2 sin (-11/6pi))$

$=(2 cos (11/6p)i, -2 sin (11/6pi))$ ,

using $cos(-a)=cos a and sin (-a)=-sin a$

$=(2 cos (2pi-pi/6), -2 sin (2pi-pi/6)$ .

$=(2 cos (pi/6), 2 sin (pi/6))$ ,

using sine in $Q_4$ is negative and cosine in $Q_4$ is positive.

$=(sqrt 3, 1)$

You ought to note that, in effect, the directions

$theta = pi/6 and theta =-11/6pi=-(2pi-pi/6)$

are the same.

For positive $theta$ , the sense of rotation is anticlockwise.

For negative $theta$ , the sense of rotation is clockwise.

What are the components of the vector between the origin and the polar coordinate (2, (-11pi)/6)(2, (-11pi)/6)?